### 63094 results for qubit oscillator frequency

Contributors: Bertet, P., Chiorescu, I., Harmans, C. J. P. M, Mooij, J. E.

Date: 2005-07-13

**frequency** in the figure). The dashed line indicates the phase-noise insensitive...**qubit** dephasing time as a function of $\delta \nu_0$. We discuss the specific...**oscillator** variables coming from the flux-dependence of the SQUID Josephson...**qubits** is known to arise because of a variety of environmental degrees... the **qubit** when ϵ = 0 , since at that point** the **average flux generated...(a)...**qubit**. Because of the coupling, the **qubit** frequency is shifted by an amount...mode-**qubit** interaction hamiltonian which, in addition to the usual Jaynes-Cummings...flux-**qubit** coupled to the plasma mode of its DC-SQUID detector. We first...**qubit** biased by Φ x and SQUID biased by current I b . (b) Simplified electrical...**Qubit** **frequency** ν q as a function of the bias ϵ for Δ = 5.5 G H z (minimum...flux-**qubit** coupled to a harmonic oscillator...**qubit** is biased at ϵ = 0 (dashed line in figure fig:nuq), it is insensitive...qubit_hamiltonian yields a **qubit** transition frequency ν q = Δ 2 + ϵ 2 ...**SQUID**-qubit system is seen as an inductance L J connected to the shunct...**frequency** shift now depends on ϵ . Since g 2 is negative (see figure fig...high-**frequency** noise from the dissipative impedance. The SQUID is threaded...lines)....0...the **qubit** is effectively decoupled from its measuring circuit. The ϵ m...flux-**qubit** is a superconducting loop containing three Josephson junctions...**qubit**. Because of the coupling, the **qubit** **frequency** is shifted by an amount...flux-**qubit** is the loop in red containing the three junctions of phases...**Frequency** shift per photon δ ν 0 as a function of I b and ϵ . The white...SQUID-**qubit** system is seen as an inductance L J connected to the shunct...the **qubit** is insensitive to** the **thermal fluctuations of** the **plasma mode...**qubit** transition **frequency** ν q = Δ 2 + ϵ 2 . The corresponding dependence ... Decoherence in superconducting **qubits** is known to arise because of a variety of environmental degrees of freedom. In this article, we focus on the influence of thermal fluctuations in a weakly damped circuit resonance coupled to the **qubit**. Because of the coupling, the **qubit** **frequency** is shifted by an amount $n \delta \nu_0$ if the resonator contains $n$ energy quanta. Thermal fluctuations induce temporal variations $n(t)$ and thus dephasing. We give an approximate formula for the **qubit** dephasing time as a function of $\delta \nu_0$. We discuss the specific case of a flux-**qubit** coupled to the plasma mode of its DC-SQUID detector. We first derive a plasma mode-**qubit** interaction hamiltonian which, in addition to the usual Jaynes-Cummings term, has a coupling term quadratic in the **oscillator** variables coming from the flux-dependence of the SQUID Josephson inductance. Our model predicts that $\delta \nu_0$ cancels in certain non-trivial bias conditions for which dephasing due to thermal fluctuations should be suppressed.

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Contributors: Dial, O. E., Shulman, M. D., Harvey, S. P., Bluhm, H., Umansky, V., Yacoby, A.

Date: 2012-08-09

**qubit** loses its quantum information due to interactions with its noisy...**frequencies** in the device....**qubit** and gives good contrast over a wide range of J . b, Exchange **oscillations**...**frequency** **oscillations** and small d J / d ϵ , a region of large **frequency**...**qubit** with an integrated RF sensing dot. a The detuning ϵ is the voltage...**qubit** is loaded and measured, and the 0 2 region where J is large but ...**qubit** during exchange oscillations. Using free evolution and Hahn echo... the **qubit** along** the **y -axis (Fig. t2stara, Fig. S1). Fig. t2starb shows ...**oscillations** and large d J / d ϵ , and a region where **oscillations** are...**qubits** are typically operated, the transitional region where J and d J...**qubit** **oscillations** to decay and setting a limit on the fidelity of quantum...**frequencies** are small, allowing the **qubit** to be used as a charge sensor...**qubit** and gives good contrast over a wide range of J . b, Exchange oscillations...single **qubit** rotations in S - T 0 and exchange-only qubits and is the ...**qubit** oscillations to decay and limits** the **fidelity of quantum control...**oscillations**. f, Charge **oscillations** measured in 0 2 . This figure portrays...**qubit**,and in metrology the **frequency** of the precession provides a sensitive...**oscillations**) of these FID **oscillations**, Q ≡ J T 2 * / 2 π ∼ J d J / d...**oscillations** in 0 2 are also primarily dephased by low **frequency** voltage...**qubit** during exchange **oscillations**. Using free evolution and Hahn echo...two-**qubit** operations in single spin, S - T 0 , and exchange-only qubits...**qubit**-based measurements. Understanding how the **qubit** couples to its environment...**qubit** **oscillations** to decay and limits the fidelity of quantum control...**frequency** and high **frequency** environmental fluctuations, respectively....**qubit**,and in metrology the frequency of the precession provides a sensitive...**qubit** to be used as a charge sensor with a sensitivity of $2 \times 10...**qubits**, a particular realization of spin **qubits** , which store quantum ...Singlet-Triplet-**Qubit**...**qubit** are grayed out. d, J ϵ and d J / d ϵ in three regions; the 1 1 region ... Two level systems that can be reliably controlled and measured hold promise in both metrology and as qubits for quantum information science (QIS). When prepared in a superposition of two states and allowed to evolve freely, the state of the system precesses with a **frequency** proportional to the splitting between the states. In QIS,this precession forms the basis for universal control of the **qubit**,and in metrology the **frequency** of the precession provides a sensitive measurement of the splitting. However, on a timescale of the coherence time, $T_2$, the **qubit** loses its quantum information due to interactions with its noisy environment, causing **qubit** **oscillations** to decay and setting a limit on the fidelity of quantum control and the precision of **qubit**-based measurements. Understanding how the **qubit** couples to its environment and the dynamics of the noise in the environment are therefore key to effective QIS experiments and metrology. Here we show measurements of the level splitting and dephasing due to voltage noise of a GaAs singlet-triplet **qubit** during exchange **oscillations**. Using free evolution and Hahn echo experiments we probe the low **frequency** and high **frequency** environmental fluctuations, respectively. The measured fluctuations at high **frequencies** are small, allowing the **qubit** to be used as a charge sensor with a sensitivity of $2 \times 10^{-8} e/\sqrt{\mathrm{Hz}}$, two orders of magnitude better than the quantum limit for an RF single electron transistor (RF-SET). We find that the dephasing is due to non-Markovian voltage fluctuations in both regimes and exhibits an unexpected temperature dependence. Based on these measurements we provide recommendations for improving $T_2$ in future experiments, allowing for higher fidelity operations and improved charge sensitivity.

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Contributors: Volkov, P. A., Fistul, M. V.

Date: 2013-05-31

**qubit** (solid green (thick) line) and tails on other **qubits** (solid red ...**qubits** display coherent quantum beatings with N different **frequencies**,...**frequencies** $\omega_1=\bar{\Delta}/\hbar$ and $\omega_2=\tilde{\omega}...th qubit (solid green (thick) line) and tails on other qubits (solid red...**qubits**. In the presence of such interaction we analyze quantum correlation...**qubits** $C_i(t)$ to obtain two collective quantum-mechanical coherent **oscillations**...**frequency** of the cavity renormalized by interaction. The amplitude of ...**qubits** are characterized by energy level differences $\Delta_i$ and we...**qubits** $C_i(t)$ to obtain two collective quantum-mechanical coherent oscillations...**qubits** display coherent quantum beatings with N different frequencies,...**qubits** (two-level systems) incorporated into a low-dissipation resonant...**qubits**...**oscillations** can be strongly enhanced in the resonant case when $\omega ... We report a theoretical study of coherent collective quantum dynamic effects in an array of N **qubits** (two-level systems) incorporated into a low-dissipation resonant cavity. Individual **qubits** are characterized by energy level differences $\Delta_i$ and we take into account a spread of parameters $\Delta_i$. Non-interacting **qubits** display coherent quantum beatings with N different **frequencies**, i.e. $\omega_i=\Delta_i/\hbar$ . Virtual emission and absorption of cavity photons provides a long-range interaction between **qubits**. In the presence of such interaction we analyze quantum correlation functions of individual **qubits** $C_i(t)$ to obtain two collective quantum-mechanical coherent **oscillations**, characterized by **frequencies** $\omega_1=\bar{\Delta}/\hbar$ and $\omega_2=\tilde{\omega}_R$, where $\tilde{\omega}_R$ is the resonant **frequency** of the cavity renormalized by interaction. The amplitude of these **oscillations** can be strongly enhanced in the resonant case when $\omega_1 \simeq \omega_2$.

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Contributors: Wallquist, M., Shumeiko, V. S., Wendin, G.

Date: 2006-08-09

**qubit** 1, and Hadamard gates H are applied to the second **qubit**....**oscillator** is entangled with **qubit** 1, at the next resonance the **oscillator**...**qubits** at their optimal points with respect to decoherence during the ...**qubit** states is achieved by sweeping the cavity frequency through the **qubit**-cavity resonances. The circuit is scalable, and allows to keep the...**qubit**-**qubit** coupling and simple gate operations. Tunable **qubit**-cavity ...**oscillator** with variable **frequency**. Our goal in this section will be to...**the** **qubit**-**qubit** coupling strength is smaller than **the** on-resonance coupling...**frequency** is sequentially swept through resonances with both **qubits**; at...**the** **qubit**-cavity resonances compared to **the** differences in **the** **qubit** frequencies...**qubit** coupling to a distributed **oscillator** - stripline cavity possesses...**qubit** states is achieved by sweeping the cavity **frequency** through the **qubit**-cavity resonances. The circuit is scalable, and allows to keep the...non-interacting qubits, and projecting on the qubit eigenbasis, | g | ...**the** qubits. Selective addressing of a **particular** **qubit** is achieved by ...**qubit**-cavity resonances compared to the differences in the **qubit** **frequencies**...two-**qubit**-cavity system, and analyze appropriate circuit parameters. We...**oscillators** represents the stripline cavity, φ 1 and φ N are superconducting... both qubits; at the first resonance the oscillator is entangled** with** ...**qubits** via tunable stripline cavity...**qubits** **frequency** asymmetry and the coupling **frequency**. Recent suggestions... to qubit 1, and Hadamard gates H are applied to the second qubit....**with **qubit 2 before swapping its state back **onto **qubit 1; free evolution...**two**-**qubit** operation. **The** qubits coupled to **the** cavity must have different... 1 , qubit 1 swaps its state **onto **the oscillator, then the oscillator ...**qubit** 1 swaps its state onto the **oscillator**, then the **oscillator** interacts...**qubits** mediated by a superconducting stripline cavity with a tunable resonance...**oscillator** through resonance with both **qubits** performing π -pulse swaps...**frequency**. The **frequency** control is provided by a flux biased dc-SQUID ... We theoretically investigate selective coupling of superconducting charge **qubits** mediated by a superconducting stripline cavity with a tunable resonance **frequency**. The **frequency** control is provided by a flux biased dc-SQUID attached to the cavity. Selective entanglement of the **qubit** states is achieved by sweeping the cavity **frequency** through the **qubit**-cavity resonances. The circuit is scalable, and allows to keep the **qubits** at their optimal points with respect to decoherence during the whole operation. We derive an effective quantum Hamiltonian for the basic, two-**qubit**-cavity system, and analyze appropriate circuit parameters. We present a protocol for performing Bell inequality measurements, and discuss a composite pulse sequence generating a universal control-phase gate.

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Contributors: Dutta, S. K., Strauch, Frederick W., Lewis, R. M., Mitra, Kaushik, Paik, Hanhee, Palomaki, T. A., Tiesinga, Eite, Anderson, J. R., Dragt, Alex J., Lobb, C. J.

Date: 2008-06-28

**phase** qubit. (a**) The** qubit junction J 1 (with critical current I 01 and...**frequency** detuning. Given the slightly anharmonic level structure of the... amplitude** **I** **r** **f at** **the** **qubit. Good** **agreement** **is** **found** **over** **the** **full ...for two-qubit experiments; the second SQUID was kept unbiased throughout...the** **qubit** **junction** **is** **obtained** **when** **L** **1 / M ≫ 1** **and** **L** **1 / L** **2 + L** **J** **2 ...the qubit; Γ ranges from 0 (white) to 3 × 10 8 1 / s (black). (b**) The**...**oscillation** **frequencies** with a simplified model constructed from the full...**qubit** junction. The measured escape rate shows Rabi **oscillations** followed...**qubit** with a 100 um^2 area junction acquired over a range of microwave...**oscillations** followed by a decay governed by multiple time constants. ...**oscillation** **frequency** Ω R , 0 1 m i n / 2 π = 540 M H z of the first...FEnergyGamma Qubit energy-level spectroscopy and tunneling escape rates...**qubit**...**oscillation** **frequency** increases as Ω R , 0 1 ≈ Ω 01 ′ 2 + ω r f - ω 0 ...**qubit**. (a) The **qubit** junction J 1 (with critical current I 01 and capacitance...**qubit**. There are two distinct phenomena that affect 0 → 1 Rabi **oscillations**...**qubit** Hamiltonian and also compare time-dependent escape rate measurements...**oscillations** plotted in the time and **frequency** domains. (a) The escape...**oscillation** **frequency** below the bare Rabi **frequency** of Ω 0 1 / 2 π = 620...**oscillation** **frequencies** Ω R , 0 1 m i n and Ω R , 0 2 m i n and (b) ...**qubit** dynamics, particularly at high power. To investigate the effects...**frequency**, and leakage to the higher excited states....of the qubit, measured at 20 mK. The scatter in the values is indicative...**oscillation** **frequency** Ω R , 0 1 at fixed bias as a function of microwave...phase** **qubit. The** **qubit** **junction** **J** **1 (with** **critical** **current** **I** **01** **and** **capacitance ... We present Rabi **oscillation** measurements of a Nb/AlOx/Nb dc superconducting quantum interference device (SQUID) phase **qubit** with a 100 um^2 area junction acquired over a range of microwave drive power and **frequency** detuning. Given the slightly anharmonic level structure of the device, several excited states play an important role in the **qubit** dynamics, particularly at high power. To investigate the effects of these levels, multiphoton Rabi oscillations were monitored by measuring the tunneling escape rate of the device to the voltage state, which is particularly sensitive to excited state population. We compare the observed **oscillation** **frequencies** with a simplified model constructed from the full phase **qubit** Hamiltonian and also compare time-dependent escape rate measurements with a more complete density-matrix simulation. Good quantitative agreement is found between the data and simulations, allowing us to identify a shift in resonance (analogous to the ac Stark effect), a suppression of the Rabi **frequency**, and leakage to the higher excited states.

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Contributors: Chirolli, Luca, Burkard, Guido

Date: 2009-06-04

**qubit** in the state "0" vs driving time τ 1 and τ 2 , at Rabi **frequency**...**qubit** states $|0>$ and $|1>$ during measurements. Our theory can be applied...**qubit** state is extracted from the **oscillator** measurement outcomes, and...**qubit**-shifted **frequencies**, Δ ω ≈ ± g . For weak driving amplitude f , ...**oscillator** **frequency** ω h o , the state of the **qubit** is encoded in the ...**oscillator** driving amplitude is f / 2 π = 20 ~ G H z and a damping rate...**qubit** in the state | 0 0 | . Correction in Δ t are up to second order....**qubit** current states is made small compared to the **qubit** gap E = ϵ 2 +...**qubit** is coupled to a harmonic oscillator which undergoes a projective...**qubit** states | 0 and | 1 , are represented for illustrative purposes by...**qubit**-dependent "position" x s are shown in the top panel. Fig2... the **qubit** QND measurement is studied in** the **regime of strong projective ...**qubit**-split **frequencies**, that is enhanced when the driving strength f ...**frequency** ϵ 2 + Δ 2 , before and between two measurements prepare the ...**qubit**-shifted **frequency**....**qubit** state is extracted from the oscillator measurement outcomes, and...**qubit** measurement. Two mechanisms lead to deviations from a perfect QND...**oscillator** to a **qubit**-dependent state. c) Perfect QND: conditional probability...**qubit** turns out to be quadratic. The **qubit** Hamiltonian is H S = ϵ σ Z ...**qubit** is coupled to a harmonic **oscillator** which undergoes a projective...**oscillator** is driven at resonance with the bare harmonic **frequency** and...**qubit** relaxation time T 1 = 10 ~ n s is assumed. Fig1...**qubit**) and quantify the degree to which such a **qubit** measurement has a...two **qubit** states produce opposite magnetic field that translate into **a qub**...**qubit**-shifted **frequencies**, the probability has a two-peak structure whose...**qubits** coupled to a circuit **oscillator**....**oscillator**, and (ii) quantum tunneling between the **qubit** states $|0>$ ...**qubit** driving time τ 1 and τ 2 starting with the **qubit** in the state | ...**qubit** coupled to a harmonic oscillator...the effect of **qubit** relaxation and **qubit** tunneling on** the **conditional ... We theoretically describe the weak measurement of a two-level system (**qubit**) and quantify the degree to which such a **qubit** measurement has a quantum non-demolition (QND) character. The **qubit** is coupled to a harmonic **oscillator** which undergoes a projective measurement. Information on the **qubit** state is extracted from the **oscillator** measurement outcomes, and the QND character of the measurement is inferred by the result of subsequent measurements of the **oscillator**. We use the positive operator valued measure (POVM) formalism to describe the **qubit** measurement. Two mechanisms lead to deviations from a perfect QND measurement: (i) the quantum fluctuations of the **oscillator**, and (ii) quantum tunneling between the **qubit** states $|0>$ and $|1>$ during measurements. Our theory can be applied to QND measurements performed on superconducting **qubits** coupled to a circuit **oscillator**.

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Contributors: Cooper, K. B., Steffen, Matthias, McDermott, R., Simmonds, R. W., Oh, Seongshik, Hite, D. A., Pappas, D. P., Martinis, John M.

Date: 2004-05-31

**qubit** in state | 0 (solid circles) and in an equal mixture of states |...**oscillations** is consistent with the spectroscopic splittings observed ...**qubits** and microscopic critical-current fluctuators by implementing a ...**qubit**'s resonant frequency. The results point to a possible mechanism ...**oscillation** periods are observed to correspond to the spectroscopic splittings...the **qubit** with strength h S / 2 . On resonance, the **qubit**-fluctuator eigenstates...**qubit** circuitry. For the **qubit** used in Fig. 2, the Josephson critical-current...**qubit**'s resonant **frequency**. The results point to a possible mechanism ... **qubit** circuitry. For the **qubit** used in Fig. 2, the Josephson critical-current...**oscillations** between Josephson phase **qubits** and microscopic critical-current...**qubit** and a microscopic resonator using fast readout...**qubit** probability amplitude first moves to state | 1 g and then **oscillates**...**qubit** with strength h S / 2 . On resonance, the **qubit**-fluctuator eigenstates... **qubit** well is much shallower and state | 1 rapidly tunnels to the right...**qubits** and demonstrate the means to measure two-**qubit** interactions in ...the **qubit** spectroscopy near Δ U / ℏ ω p = 3.55 , showing splittings of...**qubit** spectroscopy near Δ U / ℏ ω p = 3.55 , showing splittings of strengths ... We have detected coherent quantum **oscillations** between Josephson phase **qubits** and microscopic critical-current fluctuators by implementing a new state readout technique that is an order of magnitude faster than previous methods. The period of the **oscillations** is consistent with the spectroscopic splittings observed in the **qubit**'s resonant **frequency**. The results point to a possible mechanism for decoherence and reduced measurement fidelity in superconducting **qubits** and demonstrate the means to measure two-**qubit** interactions in the time domain.

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Contributors: Il'ichev, E., Oukhanski, N., Izmalkov, A., Wagner, Th., Grajcar, M., Meyer, H. -G., Smirnov, A. Yu., Brink, Alec Maassen van den, Amin, M. H. S., Zagoskin, A. M.

Date: 2003-03-20

**Qubit**...**oscillations**.... ℏ , the** **qubit** **is** **effectively** **decoupled** **from** **the** **tank** **unless** **it** **oscillates...**frequency** ω T . That is, while wide-band (i.e., fast on the **qubit** time...**qubit**, coupled to a high-quality tank circuit tuned to the Rabi **frequency**...**oscillations** in time. We report evidence for such **oscillations** in a _continuously...flux **qubit** is inductively coupled to a tank circuit. The DC source applies...**qubit** is effectively decoupled from the tank unless it **oscillates** with...the **qubit** through a separate coil at a frequency close to the level separation...**qubit** **frequency**, confirm that the effect is due to Rabi **oscillations**. ...**qubit**, coupled to a high-quality tank circuit tuned to the Rabi frequency...**frequency** of the tank is measured as a function of HF power.... the **qubit** increasing the tank’s linewidth ; these are inconsequential...The** **qubit** **was** **fabricated** **out** **of** **Al** **inside** **the** **tank’s** **pickup** **coil (Fig....**qubit** modifying the tank’s inductance and hence its central **frequency**,...**qubit** through a separate coil at a **frequency** close to the level separation... the** **potential** **profile** **of** **a** **3JJ** **qubit** **in** **the** **classical** **regime ....**qubit** inside the Nb pancake coil....**qubit** quality factor \~7000.... irradiated **qubit** modifying the tank’s inductance and hence its central... in** **the** **qubit, and** **simultaneously** **as** **a** **filter** **protecting** **it** **from** **noise... 3** **nF. The** **qubit** **has** **L** **q = 24** **pH; the** **larger** **junctions** **have** **C** **q = 3.9 ... Under resonant irradiation, a quantum system can undergo coherent (Rabi) **oscillations** in time. We report evidence for such **oscillations** in a _continuously_ observed three-Josephson-junction flux **qubit**, coupled to a high-quality tank circuit tuned to the Rabi **frequency**. In addition to simplicity, this method of_Rabi spectroscopy_ enabled a long coherence time of about 2.5 microseconds, corresponding to an effective **qubit** quality factor \~7000.

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Contributors: Chiarello, F., Paladino, E., Castellano, M. G., Cosmelli, C., D'Arrigo, A., Torrioli, G., Falci, G.

Date: 2011-10-07

**qubit** is only weakly sensitive to intrinsic noise. We find that this behaviour...**qubit** in different conditions (different oscillation frequencies) by changing...**qubit** in different conditions (different **oscillation** **frequencies**) by changing...**frequency** noise contributions, and discuss the experimental results and...**qubit** manipulation, changing the potential from the two-well “W” case ...**qubit**, indicated as double SQUID **qubit**, can be manipulated by rapidly ...**qubit** manipulated by fast pulses: experimental observation of distinct...**oscillations** with eq. envelope. The blue line in the left panel is the...**oscillations** observed for different pulse height. The measured **frequency**...**oscillations** exhibiting non-exponential decay, indicating a non trivial...**oscillation** **frequencies** observed (about 10-20 GHz), corresponding to the...used** for **the qubit manipulation, changing the potential from the two-well...**frequency** Ω / 2 π given by eq. omega for ϕ x = 0 as a function of ϕ c ... A particular superconducting quantum interference device (SQUID)**qubit**, indicated as double SQUID **qubit**, can be manipulated by rapidly modifying its potential with the application of fast flux pulses. In this system we observe coherent **oscillations** exhibiting non-exponential decay, indicating a non trivial decoherence mechanism. Moreover, by tuning the **qubit** in different conditions (different **oscillation** **frequencies**) by changing the pulse height, we observe a crossover between two distinct decoherence regimes and the existence of an "optimal" point where the **qubit** is only weakly sensitive to intrinsic noise. We find that this behaviour is in agreement with a model considering the decoherence caused essentially by low **frequency** noise contributions, and discuss the experimental results and possible issues.

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Contributors: Omelyanchouk, A. N., Shevchenko, S. N., Zagoskin, A. M., Il'ichev, E., Nori, Franco

Date: 2007-05-12

the **qubit**, and I q t the current circulating in the **qubit**. The persistent...**phase** **qubit** (Fig. 2 in ). The dependence of the frequency of these oscillations...**oscillations**....**frequency** ω = 0.612 , and the decay rate γ = 10 -3 . Low-**frequency** classical...**oscillations** around a minimum of the potential profile of Fig. fig1 as...**frequency** ω . The main peak ( ω 0 ≈ 0.6 ) corresponds to the resonance...**qubit** (Fig. 2 in ). The dependence of the **frequency** of these **oscillations**...high-**frequency**) harmonic mode of the system, $\omega$. Like in the case...**qubits** in the classical regime...**frequency**, M the mutual inductance between the tank and the **qubit**, and...**qubit** in the _classical_ regime can produce low-frequency oscillations...**qubit** in the _classical_ regime can produce low-**frequency** **oscillations**...in the **qubit** circuit produces a magnetic moment, which is measured by ...**oscillations** are clearly seen. (b) Low-**frequency** **oscillations** of the persistent...**oscillations**, the **frequency** of these pseudo-Rabi **oscillations** is much ...**frequency** $\omega$ and its subharmonics ($\omega/n$), but also at its ...**oscillations** is in the different scale of the resonance **frequency**. To ...and the **qubit**, and I q t the current circulating in the **qubit**. The persistent...a **phase** **qubit** (Fig. 2 in ). The dependence of the frequency of these ... Nonlinear effects in mesoscopic devices can have both quantum and classical origins. We show that a three-Josephson-junction (3JJ) flux **qubit** in the _classical_ regime can produce low-**frequency** **oscillations** in the presence of an external field in resonance with the (high-**frequency**) harmonic mode of the system, $\omega$. Like in the case of_quantum_ Rabi **oscillations**, the **frequency** of these pseudo-Rabi **oscillations** is much smaller than $\omega$ and scales approximately linearly with the amplitude of the external field. This classical effect can be reliably distinguished from its quantum counterpart because it can be produced by the external perturbation not only at the resonance **frequency** $\omega$ and its subharmonics ($\omega/n$), but also at its overtones, $n\omega$.

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